The present invention relates generally to signal processing, and more specifically to circuitry for improving the resolution of an analog-to-digital converter (A/D converter).
A/D converters are well known devices for providing a digital representation of an analog voltage presented at the A/D input. Typical A/D converters provide a 16-bit resolution for a single conversion, but this is not fundamental. However, depending upon the number of bits resolution provided by the A/D converter in any single conversion, the resolution is limited.
Certain classes of input signal that must be digitized are characterized by a high ratio between maximum and minimum values. An example is the signal from a Fourier transform spectrometer where it is often the case that the amount of input radiation that the spectrometer can accommodate is limited by the dynamic range of the A/D converter.
A Fourier transform spectrometer typically includes an interferometer into which an infrared beam to be analyzed and a monochromatic reference beam are directed. The interferometer includes a mechanism for each input beam to be split into two or more beam components. The beam components travel separate paths and are then recombined so as to interfere with each other. An optical element in one of the paths is scanned over a range of positions to vary the path length of one beam component relative to that of the other. The maximum excursion from zero path difference determines the maximum resolution of the spectral measurement.
There are many kinds of interferometers, but the most commonly used type for Fourier transform spectrometers is a Michelson interferometer. The interferometer has a fixed mirror and a movable mirror, and may be operated in a rapid scan mode or a step scan mode. In a rapid scan interferometer the mirror is driven at a nominally constant velocity over a portion of its travel. In a step scan interferometer, the movable mirror is moved in small increments and stopped for each measurement.
Each of the input beams is split at a beam splitter with one portion traveling a path that causes it to reflect from the fixed mirror and another portion traveling a path that causes it to reflect from the movable mirror. The portions of each beam recombine at the beam splitter, and due to optical interference between the two portions, the intensity of the monochromatic beam and each frequency component of the infrared beam are modulated as the mirror moves. For constant mirror velocity, the frequency for a particular component is proportional to the component's optical frequency and the mirror velocity. The recombined beams are directed to appropriate detectors.
The detector output represents the superposition of these modulated components, and when sampled at equal increments of mirror movement, provides an interferogram whose Fourier transform yields the desired spectrum. All these modulated components are in phase when the two paths are equal, and the resultant superposition produces a relatively huge peak in intensity, referred to as the centerburst.
The signal to noise (S/N) ratio in the interferogram is very high compared to the S/N ratio in the associated spectrum. This is because the signal contributions from the individual spectral resolution elements add linearly at the centerburst while the noise contributions add as the square root of the sum of the squares.
The monochromatic beam provides a nominally sinusoidal reference signal whose zero crossings occur each time the moving mirror travels an additional one quarter of the reference wavelength. A pulsed sampling signal is derived from the sinusoidal signal, typically from the zero crossings, and is used to trigger the data acquisition electronics to provide regularly sampled values for the interferogram. With the appropriate choice of mirror velocity, the output signal can be made to fall within a convenient range of modulation frequencies, as for example in the audio range.
The frequency of the sampling signal is referred to as the principal sampling frequency and is designated f(prin). The inverse of the principal sampling frequency is referred to as the principal sampling interval. Depending on the spectral range of interest, the sampling interval may be the distance between adjacent zero crossings of the sinusoidal signal, or may be a multiple of that distance.
The mirror velocity may be controlled and rendered substantially constant by generating a reference signal at the desired frequency f(prin) by frequency division of a signal from a crystal oscillator, and providing servo control of the mirror motion so the monochromatic signal tracks the reference signal. For a highly uniform mirror velocity, the time duration of a sampling interval (which is a constant unit of distance related to the wavelength of the monochromatic reference beam) is very nearly constant. Therefore, it is not uncommon for those in the art to use time and distance somewhat interchangeably.
Additionally, it is common to exclude data points (or not take them) for those portions of the mirror travel (typically a fraction of a millimeter) where the mirror's motion is being reversed. Thus the term "scan" should be understood generally to refer to the portion of the mirror's travel where data points are taken and used for the spectral measurement. Moreover, data acquisition typically occurs for only one direction of mirror movement.
FIG. 1 shows a prior art circuit for digitizing the analog spectrometer signal. For present purposes, the interferometer, detector, detector amplifiers, and filters as appropriate are shown as a block labeled Fourier transform spectrometer 5. It should be understood that the complete spectrometer system typically further includes the illustrated circuitry as well as various control circuits and a dedicated computer (not shown).
The analog signal from Fourier transform spectrometer 5 is communicated to the voltage input of a sample and hold (S/H) circuit 10, which provides a constant voltage level at its output when clocked by a sampling signal (at f(prin)) at its sampling input. This level is held until the A/D conversion is completed. This voltage level is communicated to an analog-to-digital A/D converter 12, which is also clocked by the sampling signal. Assuming A/D converter 12 to have an n-bit output (n=16 is typical), the characteristic resolution is one part in 2.sup.n. For a 16-bit A/D converter and analog input signals covering .+-.10 volts, the digitization increment is about 0.3 mv.
The output from the A/D converter is communicated to the dedicated computer where it is stored until all the data points in the interferogram have been acquired. The interferogram is then subjected to processing steps including a fast Fourier transform (FFT) to convert it into a spectrum. In some instances, multiple scans are made and the resultant interferograms are averaged before the FFT. For the averaging to provide a statistical improvement (increased S/N ratio), a given point on the interferogram should fall on a different part of the A/D converter's range. This will normally be the case since standard practice is to set up the spectrometer so that the noise spans at least a few digitizing increments.
In many cases, the resolution of the A/D converter sets the maximum S/N ratio that can be achieved in the spectrum in any one scan. This limitation can be partially, but not completely overcome by using a technique known as gain ranging. This technique entails increasing (for example, by a factor of 16) the analog voltage that is input to the S/H circuit and A/D converter when the mirror is away from the vicinity of the centerburst position.